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Arbitrary ColourBoundary Source # | |
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Arbitrary ColourNeedle Source # | |
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AdditiveGroup ColourNeedle Source # | |
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VectorSpace ColourNeedle Source # | |
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AffineSpace ColourNeedle Source # | |
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AdditiveMonoid ColourHalfNeedle Source # | |
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HalfSpace ColourHalfNeedle Source # | |
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SemiInner ColourNeedle Source # | |
Instance details Methods dualBasisCandidates :: [(Int, ColourNeedle)] -> Forest (Int, DualVector ColourNeedle) # tensorDualBasisCandidates :: (SemiInner w, Scalar w ~ Scalar ColourNeedle) => [(Int, ColourNeedle ⊗ w)] -> Forest (Int, DualVector (ColourNeedle ⊗ w)) # symTensorDualBasisCandidates :: [(Int, SymmetricTensor (Scalar ColourNeedle) ColourNeedle)] -> Forest (Int, SymmetricTensor (Scalar ColourNeedle) (DualVector ColourNeedle)) # symTensorTensorDualBasisCandidates :: (SemiInner w, Scalar w ~ Scalar ColourNeedle) => [(Int, SymmetricTensor (Scalar ColourNeedle) ColourNeedle ⊗ w)] -> Forest (Int, SymmetricTensor (Scalar ColourNeedle) ColourNeedle +> DualVector w) # |
FiniteDimensional ColourNeedle Source # | |
Instance details Methods entireBasis :: SubBasis ColourNeedle # enumerateSubBasis :: SubBasis ColourNeedle -> [ColourNeedle] # subbasisDimension :: SubBasis ColourNeedle -> Int # decomposeLinMap :: (LSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle +> w) -> (SubBasis ColourNeedle, DList w) # decomposeLinMapWithin :: (LSpace w, Scalar w ~ Scalar ColourNeedle) => SubBasis ColourNeedle -> (ColourNeedle +> w) -> Either (SubBasis ColourNeedle, DList w) (DList w) # recomposeSB :: SubBasis ColourNeedle -> [Scalar ColourNeedle] -> (ColourNeedle, [Scalar ColourNeedle]) # recomposeSBTensor :: (FiniteDimensional w, Scalar w ~ Scalar ColourNeedle) => SubBasis ColourNeedle -> SubBasis w -> [Scalar ColourNeedle] -> (ColourNeedle ⊗ w, [Scalar ColourNeedle]) # recomposeLinMap :: (LSpace w, Scalar w ~ Scalar ColourNeedle) => SubBasis ColourNeedle -> [w] -> (ColourNeedle +> w, [w]) # recomposeContraLinMap :: (LinearSpace w, Scalar w ~ Scalar ColourNeedle, Functor f) => (f (Scalar w) -> w) -> f (DualVector ColourNeedle) -> ColourNeedle +> w # recomposeContraLinMapTensor :: (FiniteDimensional u, LinearSpace w, Scalar u ~ Scalar ColourNeedle, Scalar w ~ Scalar ColourNeedle, Functor f) => (f (Scalar w) -> w) -> f (ColourNeedle +> DualVector u) -> (ColourNeedle ⊗ u) +> w # uncanonicallyFromDual :: DualVector ColourNeedle -+> ColourNeedle # uncanonicallyToDual :: ColourNeedle -+> DualVector ColourNeedle # tensorEquality :: (TensorSpace w, Eq w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle ⊗ w) -> (ColourNeedle ⊗ w) -> Bool # dualFinitenessWitness :: DualFinitenessWitness ColourNeedle # |
TensorSpace ColourNeedle Source # | |
Instance details Methods scalarSpaceWitness :: ScalarSpaceWitness ColourNeedle # linearManifoldWitness :: LinearManifoldWitness ColourNeedle # zeroTensor :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => ColourNeedle ⊗ w # toFlatTensor :: ColourNeedle -+> (ColourNeedle ⊗ Scalar ColourNeedle) # fromFlatTensor :: (ColourNeedle ⊗ Scalar ColourNeedle) -+> ColourNeedle # addTensors :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle ⊗ w) -> (ColourNeedle ⊗ w) -> ColourNeedle ⊗ w # subtractTensors :: (TensorSpace ColourNeedle, TensorSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle ⊗ w) -> (ColourNeedle ⊗ w) -> ColourNeedle ⊗ w # scaleTensor :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => Bilinear (Scalar ColourNeedle) (ColourNeedle ⊗ w) (ColourNeedle ⊗ w) # negateTensor :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle ⊗ w) -+> (ColourNeedle ⊗ w) # tensorProduct :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => Bilinear ColourNeedle w (ColourNeedle ⊗ w) # tensorProducts :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => [(ColourNeedle, w)] -> ColourNeedle ⊗ w # transposeTensor :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle ⊗ w) -+> (w ⊗ ColourNeedle) # fmapTensor :: (TensorSpace w, TensorSpace x, Scalar w ~ Scalar ColourNeedle, Scalar x ~ Scalar ColourNeedle) => Bilinear (w -+> x) (ColourNeedle ⊗ w) (ColourNeedle ⊗ x) # fzipTensorWith :: (TensorSpace u, TensorSpace w, TensorSpace x, Scalar u ~ Scalar ColourNeedle, Scalar w ~ Scalar ColourNeedle, Scalar x ~ Scalar ColourNeedle) => Bilinear ((w, x) -+> u) (ColourNeedle ⊗ w, ColourNeedle ⊗ x) (ColourNeedle ⊗ u) # coerceFmapTensorProduct :: Functor p => p ColourNeedle -> Coercion a b -> Coercion (TensorProduct ColourNeedle a) (TensorProduct ColourNeedle b) # wellDefinedVector :: ColourNeedle -> Maybe ColourNeedle # wellDefinedTensor :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle ⊗ w) -> Maybe (ColourNeedle ⊗ w) # |
LinearSpace ColourNeedle Source # | |
Instance details Methods dualSpaceWitness :: DualSpaceWitness ColourNeedle # linearId :: ColourNeedle +> ColourNeedle # idTensor :: ColourNeedle ⊗ DualVector ColourNeedle # sampleLinearFunction :: (TensorSpace w, Scalar ColourNeedle ~ Scalar w) => (ColourNeedle -+> w) -+> (ColourNeedle +> w) # toLinearForm :: DualVector ColourNeedle -+> (ColourNeedle +> Scalar ColourNeedle) # fromLinearForm :: (ColourNeedle +> Scalar ColourNeedle) -+> DualVector ColourNeedle # coerceDoubleDual :: Coercion ColourNeedle (DualVector (DualVector ColourNeedle)) # trace :: (ColourNeedle +> ColourNeedle) -+> Scalar ColourNeedle # contractTensorMap :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle +> (ColourNeedle ⊗ w)) -+> w # contractMapTensor :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle ⊗ (ColourNeedle +> w)) -+> w # contractTensorFn :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle -+> (ColourNeedle ⊗ w)) -+> w # contractLinearMapAgainst :: (LinearSpace w, Scalar w ~ Scalar ColourNeedle) => Bilinear (ColourNeedle +> w) (w -+> ColourNeedle) (Scalar ColourNeedle) # applyDualVector :: Bilinear (DualVector ColourNeedle) ColourNeedle (Scalar ColourNeedle) # applyLinear :: (TensorSpace w, Scalar w ~ Scalar ColourNeedle) => Bilinear (ColourNeedle +> w) ColourNeedle w # composeLinear :: (LinearSpace w, TensorSpace x, Scalar w ~ Scalar ColourNeedle, Scalar x ~ Scalar ColourNeedle) => Bilinear (w +> x) (ColourNeedle +> w) (ColourNeedle +> x) # tensorId :: (LinearSpace w, Scalar w ~ Scalar ColourNeedle) => (ColourNeedle ⊗ w) +> (ColourNeedle ⊗ w) # applyTensorFunctional :: (LinearSpace u, Scalar u ~ Scalar ColourNeedle) => Bilinear (DualVector (ColourNeedle ⊗ u)) (ColourNeedle ⊗ u) (Scalar ColourNeedle) # applyTensorLinMap :: (LinearSpace u, TensorSpace w, Scalar u ~ Scalar ColourNeedle, Scalar w ~ Scalar ColourNeedle) => Bilinear ((ColourNeedle ⊗ u) +> w) (ColourNeedle ⊗ u) w # useTupleLinearSpaceComponents :: ColourNeedle ~ (x, y) => ((LinearSpace x, LinearSpace y, Scalar x ~ Scalar y) => φ) -> φ # |
PseudoAffine ColourNeedle Source # | |
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Semimanifold ColourNeedle Source # | |
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Geodesic ColourNeedle Source # | |
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Atlas ColourNeedle Source # | |
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SemimanifoldWithBoundary ColourBoundary Source # | |
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SemimanifoldWithBoundary ColourNeedle Source # | |
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PseudoAffineWithBoundary ColourNeedle Source # | |
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ProjectableBoundary ColourNeedle Source # | |
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Geodesic (Colour ℝ) Source # | |
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Atlas (Colour ℝ) Source # | |
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SemimanifoldWithBoundary (Colour ℝ) Source # | |
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PseudoAffineWithBoundary (Colour ℝ) Source # | |
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